"There is no way this structure was made by an insect!" Or so I thought. Luckily, we have the NC Plant Disease and Insect Clinic to make the final call. The oddly shaped "case" in the first two images was created by the casemaking moth (Phereoeca uterella). The third and fourth images show a dead larva of the same species, included in the sample with the cases.
This is a very interesting (and common) insect in the Southeast, known to feed primarily on old spider webs. Research indicates they can also feed on woolen threads and cloth. Vacuuming up the cases and removing old spider webs should go a long way towards controlling this insect inside homes.
For details on biology and control, visit the following links:
Species Phereoeca uterella - Household Casebearer